PRECAUTION AND LIQUIDITY IN THE DEMAND FOR HOUSING.
BALVERS, RONALD J. ; SZERB, LASZLO
We exploit cross-sectional mortgage data to investigate the
importance of liquidity constraints and a precautionary motive in the
demand for housing. Households that are not liquidity constrained consume housing services essentially as the life cycle hypothesis suggests but with a significant precautionary component. Households that
are liquidity constrained, in terms of not meeting standard
loan-to-value or payments-to-income constraints, are similar to
unconstrained households in most respects, including the precautionary
motive, but they respond somewhat less to fluctuations in their lifetime
income--suggesting some influence of bank-induced liquidity constraints.
We additionally find, however, that banks enforce liquidity constraints
only weakly. (JEL D91, D12, R21)
I. INTRODUCTION
The benchmark theory in the economics of consumption is the life
cycle or permanent income hypothesis (LCPI) based on the work of
Modigliani and Brumberg [1954] and Friedman [1957]. Its empirical
validity is sometimes questionable, especially when compared against
alternatives that incorporate liquidity constraints or the precautionary
motive for saving. See, for instance, Deaton [1992] for a survey.
Rejection of the LCPI may, however, be just a manifestation of the poor
quality of consumption data. At the micro level, these data are
typically subject to the reporting biases and omissions inherent in
consumer surveys. There are further difficulties in measuring a desired
stream of consumption services: nondurable consumption goods are a small
fraction of total consumption and, in the case of food essentials,
hardly a consumer choice variable; durable consumption goods have the
feature that they are lumpy and that the consumption services at any
point in time are hard to measure.
We propose to test the LCPI at the micro level with a quite
different type of data. The data are obtained from the Residential
Mortgage Finance Database collected by the National Association of
Realtors. They are based on actual home purchases and the associated
mortgage transactions reported by realtors and thus avoid some of the
reporting biases of the consumer surveys. More important, they allow us
to accurately identify households that, in principle, have instantaneous access to additional liquidity by lowering the down payment for the
house purchase or increasing the size of the loan. Further, the purchase
of a house provides an accurate measure of a relatively large fraction
of consumption services obtained for a medium to long horizon and
measured at the time of the consumption decision. Although our data also
have some serious shortcomings, they allow a look at the LCPI from an
unconventional vantage point.
Perhaps the most influential study employing the standard consumer
survey in testing the LCPI at the micro level is that of Hall and
Mishkin [1982]. It examines food expenditure from the Panel Study of
Income Dynamics. One of their key results is that consumption tracks
income more closely than would be expected under the LCPI. They
demonstrate that this result could be explained by assuming a group of
liquidity-constrained consumers, consuming their income at each point in
time, of 20% of the total sample. Some of the drawbacks of this study
are the use of food expenditures to represent consumption, the
underreporting of income, and absence of proper wealth data inherent in
the consumer survey, and the associated inability to individually
separate liquidity-constrained consumers from the rest of the sample.
Several previous studies have attempted to improve on this way of
testing the LCPI by examining other data sets. Bernanke [1984] used data
on durable consumption goods (automobiles) to overcome the drawbacks of
using food consumption in the Hall and Mishkin study. His results
support the LCPI but are still suspect because of possible reporting
biases and the lack of good wealth and savings observations. Hayashi
[1985] employs the Survey of Financial Characteristics of Consumers
conducted by the Board of Governors of the Federal Reserve System, which
includes detailed information about income and wealth variables. These
data enable him to identify as consumers who are not liquidity
constrained those who save a lot at the current time. In these data, the
constrained households consumed less than predicted by the results for
the whole sample, suggesting that borrowing constraints were effective,
thus providing evidence against the LCPI. As noted by Deaton [1992,
155], Hayashi's data do not contain consumption, so it must be
inferred from disposable income and asset transactions. In addition to
being susceptible to reporting biases, the procedure also misrepresents
the service flow of durable consumption by measuring it as the total
amount spent on durable consumption goods (this would be particularly
inappropriate if a house was bought!).
Jones [1990] is similar to our study in the sense of using housing
demand to test the LCPI. His hypothesis is that liquidity-constrained
households should base their housing demand mostly on current net wealth
whereas nonconstrained households should also be sensitive to their
current labor income, as representative of lifetime earnings. The study
is conducted based on the young households (head of household age up to
34 years) in the Canada Survey of Consumer Finances. This data set
provides good information about the households' asset positions but
has some drawbacks in not providing the purchase date and price of the
house and using reported market value for the price of the house.
Jones's results show that net wealth is more important than
income in explaining the housing demand of these young Canadian
households. His results thus support the importance of liquidity
constraints as contrasted against the pure LCPI hypothesis. Note,
however, that Jones's basic interpretation of the LCPI does not
include a precautionary motive in the determination of consumption. [1]
The shortcomings of our data will be discussed in section III, but
the main advantages are that the surveys are completed by realtors based
on actual transactions, that housing prices are observed at the exact
time of purchase, that the dowupayment is reported without bias and may
serve as an adequate measure of initial wealth, and that precise
identification of nonconstrained households is possible.
Our data allow us to check by maximum likelihood corrected for
truncation bias whether the permanent income elasticity equals one, as
suggested by the life cycle hypothesis; whether a precautionary savings
motive is identifiable; whether liquidity constraints matter to
households or banks; and whether different groups of borrowers have
different consumption patterns.
II. THEORY
We employ a basic model of the LCPI augmented with a precautionary
savings motive. Xu [1995] decomposed the precautionary motive into one
part related to income uncertainty and one part related to liquidity
considerations. As we are able to identify households without current
liquidity problems, and, likely, also without anticipated future
liquidity problems, we can theoretically focus on the precautionary
motive as related to income uncertainty only.
To derive a simple empirically testable equation in the absence of
liquidity constraints the most crucial simplifying assumptions are the
following: (1) the real rate of interest is equal to the rate of time
preference; (2) the elasticity of substitution between housing services
and other consumption services is constant; (3) uncertainty about income
takes the form of a one-time shock realized at some time in the future.
Consider then the life cycle consumption problem of a typical household:
(1) [Max.sub.[[{[H.sub.s], [C.sub.s]}.sup.T-1].sub.0]
E[[[[sum].sup.T-1].sub.j=0] [[lgroup][frac{1}{1 + [rho]}][rgroup].sup.j]
U([Z.sub.j])].
(2) s.t.
[Z.sub.t] = [[[[alpha].sup.[frac{1}{[sigma]}]]
[[H.sup.[frac{[sigma] - 1}{[sigma]}]].sub.t] + [(1 -
[alpha]).sup.[frac{1}{[sigma]}]] [[C.sup.[frac{[sigma] -
1}{[sigma]}]].sub.t]].sup.[frac{[sigma]}{[sigma] - 1}]].
(3) [W.sub.t+1] = (1 + r)[W.sub.t] + [Y.sub.t] - [Z.sub.t].
(4) [Z.sub.t] = [C.sub.t] + (r + [delta])
[[p.sup.H].sub.t][H.sub.t].
Equation (1) represents the standard time-separable utility
function with finite lifetime. Expectations are taken conditional on
information at time zero; life duration, T, differs among household
heads depending on current age. The consumption index at time t,
[Z.sub.t], is a constant elasticity by substitution (CES) function of
housing consumption, [H.sub.t], and other consumption services,
[C.sub.t], with elasticity of substitution equal to [sigma] as given in
equation (2). Real wealth (with consumption services as the numeraire),
[W.sub.t], evolves according to equation (3), with real interest rate r
and stochastic real income, [Y.sub.t]. From basic duality theory real
expenditure can be written as [Z.sub.t] and is given by equation (4) as
the quantity of consumption plus the relative price of housing times the
measure of housing quantity.
The relative price of housing is given as the Jorgensonian user
cost (r + [delta])[[p.sup.H].sub.t] per unit of housing, which is
similar for home-owners as well as renters (we ignore tax effects), as
the real interest cost plus upkeep (depreciation) times the unit price
of the house in real terms. Actual costs for the owner equal nominal
interest minus the appreciation of the house in nominal terms, which
equals the real interest rate if the housing market provides a proper
hedge against inflation. If the house appreciates in real value terms,
this should be incorporated in the [delta] term and may potentially lead
to a negative [delta].
The uncertainty concerning future income is assumed to take the
following simple form in order to model a precautionary motive for
saving with relatively few additional complications
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
with [eta] [greater than] 0 and E([eta]) = 1. [2] The income
uncertainty is resolved completely at future time s. The household
making decisions at time 0 thus faces lifetime income uncertainty that
is rationally anticipated to be resolved at (and no sooner or later
than) a specific time s [greater than] 0. Since by assumption we have r
= [rho], it follows straightforwardly that [3]
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The expressions for Z--the consumption level before the income
uncertainty is revealed--and Q([eta])--the fraction of additional
consumption after the income uncertainty is revealed--will be examined
in the following. Solving the current budget constraint in equation (3)
using the fact that [W.sub.T+1]. = 0 to obtain the lifetime budget
constraint, and making use of equation (6) yields:
(7) Z [lgroup]1 + [frac{Q([eta])[[(1 + r).sup.T-s] - 1]}{[(1 +
r).sup.T] - 1}][rgroup]
= PI([eta]),
where the left-hand side of equation (7) represent the per-period
average present value of consumption expenditure from current time until
death at time T and the right-hand side represents Deaton's [1992]
formalization of the concept of permanent income, expressed in our
framework as [4]
(8) PI([eta]) = [frac{r[(1 + r).sup.T]}{[(1 + r).sup.T] - 1}]
X [lgroup][W.sub.0] + [[[sum].sup.s].sub.j=1] [frac{Y}{[(1 +
r).sup.j]}] + [[[sum].sup.R].sub.j=s+1] [frac{[eta]Y}{[(1 +
r).sup.j]}][rgroup].
Optimal housing demand can be obtained from a two-stage budgeting
process. First,
(9) [H.sub.t] = [alpha][([[p.sup.H].sub.t]).sup.-[sigma]]
[Z.sub.t].
Taking expectations in equation (7), and using equation (9)
together with equation (6) for t = 0, yields the demand for housing at
time 0
(10) [H.sub.0] = [frac{[alpha]}{[(r +
[delta]).sup.[sigma]]}][([[p.sup.H].sub.0]).sup.-[sigma]] E[PI([eta])]
x [[lgroup]1 + [frac{E[Q([eta])][[(1 + r).sup.T-s] - 1]}{[(1 +
r).sup.T] - 1}][rgroup].sup.-1].
We next analyze the term in large parentheses in equation (10). The
first-order conditions imply that consumption smoothing is attempted
even for the period during which uncertainty is resolved. In particular,
(11) U'(Z) = E(U'{Z[1 + Q([eta])]}),
which determines the distribution of Q([eta]) together with
equations (7) and (8).
The coefficient of variation of permanent income, [gamma] [equiv]
[[sigma].sub.PI]/E[PI([eta])] may be obtained from equation (8). The
appendix shows that [gamma] affects E[Q([eta])] or the term in
parentheses in equation (10) positively given a "prudent"
consumer as clarified by Kimball [1990]; if [omega] indicates the degree
of prudence of the consumer, then an increase in [omega] also affects
E[Q([eta])] positively. This term is further affected by T and
E[PI([eta])] but the effect of either is ambiguous. The appendix
derives, however, the effects for a constant relative risk aversion utility function, which yields
(12) 1 + [frac{E[Q([eta])][[(1 + r).sup.T-s] - 1]}{[(1 + r).sup.T]
- 1}]
= q([gamma], [omega], T),
with partial derivatives, [q.sub.[gamma]] [greater than] 0,
[q.sub.[omega]] [greater than] 0, and [q.sub.T] [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN ASCII] [q.sub.E(PI)] = 0 and r and s are treated as
fixed parameters. These results are less specific than those in
Caballero's [1991] elegant model but more desirable empirically, as
they do not rely on the implausible case of constant absolute risk
aversion.
III. FROM THEORY TO MEASUREMENT
Based on the above model, we will investigate the determinants of
the demand for housing. Before we proceed to the estimation, however, we
will first describe the data and, subsequently present the model in a
form that is estimable from these data.
Data Description
The data available to us from the Residential Mortgage Finance
Database for the years 1988, 1989, and 1990 were collected by the
National Association of Realtors through surveys completed by realtors
in large metropolitan areas. These data consist of information from
mortgage applications and other sources available to the realtors at the
time of the closing of the purchase of a primary home. Variables
included are purchase price of the house, down payment, loan amount,
mortgage rate and type of mortgage, family size, borrower income, and
age.
The total numbers of observations in the data set are 1,228, 1,138,
and 922 for 1988, 1989, and 1990, respectively. All three years in our
data set are similar in terms of representing low and stable inflation.
We thus combine the sample points from all three of these periods.
Sample points containing second mortgages, buy-downs, buyers over 65
years old, no or negative down payment, missing data, or obviously
incorrect information are excluded. This leaves us with a total sample
of 2,364 observations.
The data have several drawbacks. (i) They are not a panel and thus
provide only current income information. (ii) The data provide limited
information about nonfinancial borrower characteristics. Information
about occupation, race, and education is not available, and we rely on
age, and family size (as in Jones [1990]), and the unexplained component
of the choice of mortgage type, to control for individual household
taste variation. (iii) No information about income components and wealth
is available. Nonhuman wealth must be measured by the down payment,
which is certainly a questionable approximation but at least one that is
based on an actual market transaction rather than obtained by household
survey. And (iv) all households in our sample are homeowners, posing a
sample selection problem that is difficult to correct.
On the other hand, the data offer several advantages. (i) They
include diminished reporting bias due to provision by professionals
based on recent market transactions; (ii) timeliness of the observations
in terms of measuring housing consumption at the time of the transaction
so that inertia has not yet contaminated the reliability of the
observation as a measure of desired consumption (see Grossman and
Laroque [1990] on the importance of inertia in the demand for illiquid assets); (iii) our data are homogeneous, consisting entirely of
homeowners in large metropolitan areas during a relatively
noninflationary period; and (iv) most important, our data allow
identification of nonconstrained borrowers as those who, currently,
could have obtained a larger loan from the bank or could have lowered
their down payment because they face no loan-to-value or
payment-to-income constraint. In addition, our introduction of these
data to the study of consumption provides a new perspective.
Another data source, the Mortgage Interest Rate Survey (MIRS), is
provided by the Office of Thrift Supervision. This data set provides
monthly average regional house prices, which are used to construct our
housing price index variable. Data on actuarial life expectancy, average
taxes for the income brackets, and inflation rates are drawn from
various issues of the Statistical Abstracts of the United States (years
1990-93).
Empirical Specification
In the following, we take in all cases time 0 to be the time of
purchase of the house and omit the time subscript. To obtain the
empirical model as it applies to individual take logs in equation (10)
after substituting in equation (12). Rearranging to replace housing
units for individual i, [H.sub.i], by the observable purchase price of
the house, [[p.sup.H].sub.i][H.sub.i], yields
(13) ln [[p.sup.H].sub.i] [H.sub.i]
= ln[[(r + [[delta].sub.i]).sup.-[[sigma].sub.i]]
+ (1 - [[sigma].sub.i])ln [[p.sup.H].sub.i] + ln E([PI.sub.i])
- ln q([[gamma].sub.i], [[omega].sub.i], [T.sub.i]) + ln
[[alpha].sub.i].
Equation (13) can be used directly for estimation purposes with the
following adjustments. First, we "linearize" the precautionary
term, setting ln q([[gamma].sub.i], [[omega].sub.i], [T.sub.i]) =
[[gamma].sub.i] + [[omega].sub.i][[gamma].sub.i] + [T.sub.i]. Our choice
between log-linear or linear variable specification is dictated by the
ease of interpretation of the regression coefficient for the variable in
question. The interaction between prudence and variability appears to be
reasonable intuitively and is motivated in part by the constant relative
risk aversion (CRRA) utility form discussed in the appendix. Second, we
take the parameters [[sigma].sub.i] (elasticity of substitution between
housing and consumption) and [[delta].sub.i] (maintenance expenses) to
be constant across individuals; variations in [[delta].sub.i] (related
to differences in ability for housing maintenance and repair) may be
captured by a zero-mean random error [[epsilon].sub.i]. Third, we
approximate differences in [[alpha].sub.i] (utility weight of housing)
by available household characteristics like household size ([HS.sub.i])
and age. Equation (13) then becomes, in regression format [5]
(14) ln ([[p.sup.H].sub.i] [H.sub.i])
= [b.sub.0] + [b.sub.1] ln [[p.sup.H].sub.i]
+ [b.sub.2] ln E([PI.sub.i]) + [b.sub.3][[gamma].sub.i]
+ [b.sub.4][T.sub.i] + [b.sub.5][HS.sub.i] +
[b.sub.6][[omega].sub.i][[gamma].sub.i]
+ [[epsilon].sub.i].
Our hypotheses are simply [b.sub.1] [less than] 1 (implying that
the intraperiod demand elasticity for housing, [sigma], exceeds 0);
[b.sub.2] [greater than] 0, or [b.sub.2] = 1, the first being a weak
test of the LCPI hypothesis, the second being a test for the
narrowly-defined version of the LCPI hypothesis as derived in our theory
section; [b.sub.3] [less than] 0, implying that a precautionary motive
for postponing consumption is present; and [b.sub.6] [less than] 0,
testing the hypothesis that more prudence will imply the choice of a
smaller house. Other than [b.sub.0] (which we expect to be positive),
the coefficients are not theoretically constrained; in particular the
effect of age on the home purchase consists of both a taste effect and a
precautionary effect, which cannot be separately identified.
Variable Definitions
Before we present our regression results, we define the variables
used in regression equation (14). The endogenous house value variable
[[p.sup.H].sub.i] [H.sub.i] is given by the price of the house (the
principal residence in all cases) at the time of purchase by household
i. The price index [[p.sup.H].sub.i] is calculated from the MIRS data.
Each observation is differentiated by region (northeast, north central,
south, and west) and by month and is normalized by the west regional
average house price for January 1988, the first month of the sample
period. (The same method is used by Brueckner and Follain [1989]).
To measure E([PI.sub.i]), we set time of retirement in equation (8)
at R = 65; our measure for each household of initial wealth [W.sub.0] is
provided by the down payment, [D.sub.i], for the house purchase. While
not a perfect measure, it is based on the actual market transaction of
the house purchase as reported by the realtor. [6]. We further set s
(the time until resolution of the income uncertainty) = 5 and r (the
discount rate) = 0.03 (similar to Caballero [1990], who sets r = 0.04,
and Hubbard, Skinner and Zeldes [1995], who set r = 0.03) in equation
(8) and E([eta]) (the expected proportionate value of income upon
realization of the income uncertainty) = 1 to obtain expected permanent
income. [7]
The income variable [Y.sub.i] used in the permanent income measure
includes noninterest family income after taxes earned before the
purchase of the house; it does not include an imputed rental income.
Income is not broken down in components; no wealth or tax information is
available. Taxes are proxied based on the tax brackets provided in the
Statistical Abstract for the relevant years. Income is stratified and
given in ten brackets ranging from less than $25,000 to $100,000 or
more. For the interior brackets, income is calculated as the midpoint of
the bracket. Income of less than 25,000 is set to 20,000 and income
greater than 100,000 is set to 120,000--20% less and more, respectively,
than the extreme points of the brackets. This selection was tested in
our various specifications, but income dummies inserted for the lowest
and highest income bracket were found to be insignificant.
We use [[gamma].sub.i], the coefficient of variation in permanent
income to help represent q (Caballero [1990] also uses the coefficient
of variation to measure permanent income risk). Employing the definition
of the coefficient of variation and equation (8), we measure
[[gamma].sub.i] as
(15) [[gamma].sub.i] =
[[sigma].sub.[eta]][lgroup][frac{([y.sub.i]/r)[[(1 + r).sup.R-s] -
1]}{[(1 + r).sup.R]}][rgroup]
x [[lgroup][D.sub.i] + [frac{([Y.sub.i]/r)[[(1 + r).sup.R] -
1]}{[(1 + r).sup.R]}][rgroup].sup.-1],
treating [[sigma].sub.[eta]] as constant across individuals and
using the same parameter values as for our measure of E([PI.sub.i]). Our
data limitations imply that no direct measure for income uncertainty is
available. In employing the expression for the coefficient of variation
of lifetime income in equation (15), we thus must keep
[[sigma].sub.[eta]] constant across individuals. Cross-sectional
differences in the coefficient of variation arise solely from
differences in household wealth relative to income and age.
The variable [T.sub.i] captures age variation in the precautionary
variable [q.sub.i]([[gamma].sub.i], [[omega].sub.i], [T.sub.i]) and age
effects on the utility weight on housing [[alpha].sub.i]. Age is given
in eight brackets where, as with the income variable, we use the
midpoint, except for the group under 25 which we set to 22 (about the
midpoint between 18 and 25), and the group over 65 years, which is very
small and is thrown out. We obtain (expected) time of death [T.sub.i] as
the actuarial life expectancy conditional on the age of the head of the
household. Household-specific taste variation is further approximated
using the variable, [HS.sub.i], for household size.
To better control for variation in [q.sub.i] across households, we
additionally use, in one of our regressions, the unexplained part of the
choice of mortgage type, fixed-rate mortgage (FRM) or adjustable rate
mortgage (ARM), as a measure of consumer prudence [[omega].sub.i] (where
we tentatively presume a negative correlation between the choice of an
ARM and prudence). We calculate this variable based on a 0, 1
designation of FRM (assigned one) versus ARM (assigned zero). We run a
probit regression explaining mortgage type from the same variables that
explain house value (ignoring, of course, the [[omega].sub.i] variable)
but, as a price variable, replacing the housing price index by the
difference between the relevant fixed mortgage rate and variable
mortgage rate. The error in this probit regression is used as our proxy
for [[omega].sub.i].
In selecting the sample to exclude constrained households we define
constraints in standard fashion as follows. The loan-to-value (LTV)
ratio is defined as the ratio of the mortgage loan
([[p.sup.H].sub.i][H.sub.i] - [D.sub.i]) to the purchase price of the
house ([[p.sup.H].sub.i][H.sub.i]). The payment-to-income (PTI) ratio is
defined as the ratio of the mortgage payment (one over the term of the
mortgage plus the mortgage rate time the mortgage loan) to income
([Y.sub.i]). [8]
Summary statistics for our data, providing means and standard
variations of key variables, are provided in Table I.
IV. RESULTS
Unconstrained Households
To evaluate the precautionary-motive-extended LCPI, we focus first
on those households that are guaranteed not to be subject to LTV or PTI
constraints. These consumers have two characteristics that make them
likely to be proper LCPI consumers: (1) the amount spent on the home
purchase is not influenced by the bank; (2) current and anticipated
future liquidity considerations must be minor, since these households
could have obtained a larger (mortgage) loan from the bank or lowered
their down payment and would qualify for a home equity loan if future
liquidity needs would arise.
We consider those households with a PTI [geq] 0.28 or an LTV [geq]
0.95 as constrained. [9] (Although some banks maintained tighter
constraints in the 1980s, it is safe to say that households then could
easily find a bank that employed the milder constraints). However, we
also consider the tighter constraints of PTI [geq] 0.25 and LTV [geq]
0.80. The latter is relevant because a down payment of 20%, implying LTV
= 0.80, allows the household to avoid paying private mortgage insurance.
Defined as unconstrained is any household purchasing a home of less than
95% of the maximum value allowed subject to the LTV and PTI constraints.
Other authors, such as Hayashi [1985] and Jones [1990], have sometimes
used tighter criteria to weed out potentially constrained households,
but the constraints we consider here appear to be sufficient, and
tighter constraints would remove too many sample points. For the first
set of PTI and LTV constraints, 1,605 unconstrained households remain in
the sample; for the tighter PTI and L TV constraints, 616 unconstrained
households remain.
For both sets of constraints, regression results by maximum
likelihood are corrected for selection bias resulting from truncation of
the endogenous house value. The results are presented in Table II,
columns 1 and 2. [10] For the larger sample (fewer households are
excluded as being constrained), the price elasticity, [b.sub.1] - 1, is
as expected: a point estimate equal to - 0.42, significantly different
both from 0 and from 1. This is of similar magnitude compared to the
results obtained for cross-sectional data by Brueckner and Follain
[1989], Harrington [1989], and Sacher [1993] of -0.52, -0.42, and -0.72,
respectively. The permanent income coefficient equals 0.94, is highly
significant and positive as expected, further, it does not significantly
differ from 1 (at the 5% level) as suggested by the model. The
precautionary variable is significantly negative, that is, a higher
coefficient of variation of permanent income significantly lowers
current consumption (and raises precautionary savings). The resul ts for
the smaller sample (retaining only those households that were clearly
liquid enough to be able to avoid purchasing private mortgage
insurance--house price less than 95% of the value allowed subject to the
LTV [less than] 0.80 and PTI [less than] 0.25 constraints)--are
qualitatively similar as seen by comparing column 2 to column 1.
Thus, the strict version of the LCPI must be rejected in favor of
the model with a precautionary savings motive as is consistent with the
numerical results of Zeldes [1989], Caballero [1990], Hubbard, Skinner,
and Zeldes [1995], and others. The finding of a precautionary motive is
also consistent with the empirical results of Haurin and Gill [1987] in
the context of the demand for housing, who find that housing consumption
falls with the level of income uncertainty. Our results, however, are
not consistent with the results of Haurin [1991], who, with data more
suitable for measuring income uncertainty, does not detect an effect of
income uncertainty on housing consumption.
Next, we examine if liquidity constraints affect the results. We
compare the results for the samples of unconstrained households (1,605
and 616 households) to the results for the full sample of 2,364
households. (Note that we will be able to directly compare constrained
and unconstrained households at a later point, but that the current
comparison is valuable as it is hard to establish which households are
truly constrained). Simple ordinary least squares (OLS) regression
produces the results displayed in Table II, column 3. These results
again support the extended LCPI and are surprisingly similar to the
results for the unconstrained households: a similar estimated price
elasticity, a permanent income coefficient that is not significantly
different from 1, and a significant precautionary effect.
The importance of the precautionary variable in all three of the
(sub)samples provides a potential explanation for the result in Jones
[1990] that net wealth affects consumption positively for given income.
In our view, higher net wealth relative to current income means that a
larger share of lifetime income is certain. Thus, precautionary demand
for savings falls--current consumption is higher. Jones attributes the
positive effect of net wealth on current consumption (for given lifetime
income) to a liquidity effect: higher net wealth relaxes a liquidity
constraint so that current consumption can be higher. In the next
section, we will be able to better evaluate Jones's explanation
relative to ours by examining directly the behavior of constrained
households relative to unconstrained households.
One of the limitations of the LCPI as applied to housing demand is
that it ignores the portfolio implications of the mortgage loan and the
home as an asset. These portfolio implications in the demand for
housing, and other illiquid durable consumption goods, are examined for
instance by Henderson and Ioannides [1983], Plaut (1987] and Grossman
and Laroque [1990]. To the extent that younger households who are
first-time home buyers typically have too few nonhousing assets to be
seriously concerned about the role of house and mortgage loan in their
portfolios, our model is more likely to apply to young households. [11]
Thus, to check the robustness of our results, we further limit the
unconstrained household sample by excluding all households with head
older than 34 years and those who are not first-time home buyers.
(Thirty-four years is the typical cut-off for young versus old
households; see, for instance, Jones [1990], Duca and Rosenthal [1993],
or Sheiner [1995]). This reduces the sample of the unconstrained from
1,605 to 352. The results for this subsample are displayed in Table II,
column 4. These results are very similar to our previous results with
the proviso that the precautionary effect now becomes insignificant,
although its coefficient value remains similar.
Before considering constrained households, we take advantage of the
specifics of our data set to use the unexplained part of the choice of
mortgage type as a proxy for [[omega].sub.i], household prudence, where
home owners with unexplained preference for ARMs are tentatively
identified as less cautious. Column 5 in Table II displays the results
when a "prudence" variable is added to the basic regression of
column 1. This variable is defined as the product of the coefficient of
variation of permanent income ([[gamma].sub.i]) times the unexplained
part of the adjustable versus fixed rate mortgage choice (which proxies
for [[omega].sub.i]). It is expected to have a negative impact on house
value, if households with an unexplained preference for FRMs are more
cautious.
The results in column 5 are consistent with the results in column
1. Although the prudence variable has a negative effect in column 5, the
coefficient is not significant. Possible explanations for the lack of
significance are that (a) for certain households FRM contracts may in
fact be riskier than ARM contracts, as discussed in Szerb [1996]; or
that (b) the ARM choice is less indicative of lack of caution than it is
indicative of the household's expectation to move in a relatively
short time. Specifically, a household expecting to move quickly is more
likely to take the ARM, which typically has a rate that is initially
lower than the FRM rate; but such a household may also be more likely to
buy a smaller house. In this case, the "mobility" effect may
offset the "prudence" effect. The mobility effect may be less
relevant in our sample, where households acquire the mortgage when they
buy the house, since it is rarely optimal to buy a new home if one
intends to move shortly thereafter.
In further robustness checks, we replaced our permanent income
variable with income and with the down payment. In both cases, the
results deteriorated. We also added income and the down payment
separately to the regression including the permanent income variable,
but this led to serious multi-collinearity problems. These results are
not presented.
Liquidity-Constrained Households and an Endogenous Switching
Approach
In the housing literature, recent work by Sheiner [1995] shows that
liquidity constraints of renters are an important factor in tenure
choice, whereas Duca and Rosenthal [1993] report that 30% of young
households in the Survey of Consumer Finances consider themselves
liquidity constrained. We consider the housing choice of new homeowners
that are likely to be liquidity constrained based on the
realtor-provided information in our data set.
Although it is fairly straightforward in our data set to select
households that are definitely unconstrained (we essentially observe
excess liquidity), it is much more difficult to identify definitely
constrained households (we cannot observe a "shortage" of
liquidity; for instance, due to possible government guarantees or the
possibility that not all current wealth was used as down payment). We
thus consider as constrained, fairly arbitrarily, those households that
buy a home worth more than 105% of the maximum value allowed by the LTV
and PTI constraints. The results of the regressions, again correcting
for truncation bias, are presented in Table III, column 6--reporting
results for the complement of the data used in column 1 minus all
households with homes valued between 95% and 105% of the amount implied
by LTV = 0.95 and PTI = 0.28--and column 7 --reporting results for the
complement of the data used in column 2 minus all households with homes
valued between 95% and 105% of the amount implied by LTV = 0.80 and PTI
= 0.25. The results are not much different from the results for the
unconstrained households. The main difference is that the permanent
income coefficients now are significantly less than i and equal to 0.73
for the smaller sample (565 households) and 0.84 for the larger sample
(1,298 households).
The degree of caution is somewhat lower for the constrained
households in both sub-samples. If the view of Jones [1990] were
correct, then our precautionary variable would proxy for the (inverse of) net wealth and would imply an apparently stronger
"precautionary" effect for constrained households. If
anything, however, the precautionary variable is less important for
constrained households. Thus, the precautionary effect seems to dominate
the liquidity effect. Nevertheless, the lower value for the permanent
income coefficient in the constrained households case suggests that
liquidity does matter to some extent.
To further examine the nature of a possible liquidity effect, we
again consider the ARM versus FRM households. Xu [1995] has shown that,
in the presence of potential liquidity constraints, two types of
precautionary savings should occur: one that anticipates potential
negative adjustments to lifetime wealth and one that anticipates
potential liquidity shortages. Although holders of ARMs need not be less
cautious in terms of lifetime wealth as we found earlier (and as
emphasized theoretically by Szerb [1996]: ARMs tend to be less risky
than FRMs if inflation premia are more variable than real interest
components), holders of ARMs are definitely less cautious in terms of
liquidity problems. A household facing liquidity shortages would do well
to consider the FRM, in spite of the typically lower expected interest
costs offered by the ARM, to avoid potential increases in interest
payments that would exhaust liquidity. If a liquidity-constrained
household nevertheless chooses the ARM, this suggests a low degree o f
caution.
If liquidity considerations are important the above discussion
suggests that liquidity constrained households that are ARM holders have
a low degree of caution (as discussed earlier: if they are just more
likely to move soon, why would they purchase a new home at this point in
time?). They therefore should respond less to changes in the variation
of their lifetime income than should liquidity-constrained FRM holders.
The regressions for constrained households presented in Table III,
columns 6 and 7, include an interaction variable for the coefficient of
variation of permanent income (CFVAR) and the mortgage choice (ARM
choice equals 0) as in column 5, Table II. The results reveal that the
interaction variable is insignificant. This further supports the view,
from the perspective of the households at least, that liquidity
considerations are not crucial.
Typically, households that are younger are more likely to be
liquidity constrained. This is one reason that many consumption studies
have been limited to young households. To a large extent, our selection
procedure for constrained households is more precise than a pure
age-based criterion, since it looks at income and wealth variables that,
in principle, directly determine liquidity. Given, however, that our
measures are imperfect, age may be helpful as an additional sample
selection criterion in identifying constrained households. Thus, we
further restrict the sample based on age, in this case by retaining from
the subsample in column 7 only those constrained households who are
first-time home buyers and whose head is 34 years or younger, reducing
sample size from 1,298 to 553. This selection criterion again also has
the advantage of limiting the sample to young households, who are less
likely to choose house and mortgage based on portfolio considerations
and for whom therefore the down payment is more like ly to be close to
current wealth. The results are displayed in column 8. Results are
similar to those in columns 6 and 7 except that the permanent income
coefficient is now 0.87, a little closer to i. Further, the
precautionary variable becomes insignificant as is the case for the
age-restricted sample of unconstrained households in column 4, Table
II.. It appears that the basic LCPI model may indeed better describe the
behavior of young households.
Although households may not base consumption choices on current or
expected future liquidity positions, banks have to deal with information
asymmetries and may take LTV and PTI constraints seriously. From this
perspective, a household chooses the value of the house when
unconstrained, whereas a bank specifies the value of the house when the
household is constrained. One may then think of the regression model as
one of endogenous switching, where the outcome is the optimal consumer
choice given in equation 13 if no constraint is binding and the outcome
is the constrained value (set by the bank) when either the LTV
constraint or the PTI constraint is binding.
The value set by the bank is modeled as
(16) ln[([[p.sup.H].sub.i][H.sub.i]).sub.bank]
= [c.sub.0] + [c.sub.1] ln([Hmax.sub.i]) + [[nu].sub.i],
where the Hmax variable indicates the highest value of the house
allowed by the bank given the LTV constraint of 0.95 and the PTI
constraint of 0.28. The error term is assumed to be white noise. It
would be expected that [c.sub.0] = 0 and that [c.sub.1] = 1. The value
of the house observed equals the minimum of the left-hand side of
equation (14) and the left-hand side of equation (16). This model then
is a standard "disequilibrium" model as described by Maddala
[1983, 2961.
Estimation of the model by maximum likelihood would not converge.
We accordingly employ the suggestion of Goldfeld and Quandt [1975] to
impose a restriction among the standard errors of the separate
regressions. As the standard errors of both equations estimated by OLS
are approximately equal we impose this equality restriction. The results
are presented in Table III, column 9. The result for the constrained
households is that the coefficient [c.sub.0] is significantly positive,
whereas [c.sub.1] = 0.43, which is significantly positive but less than
1. Thus, banks have a significant but limited impact on the housing
choice of constrained households: a 1% decrease in the maximum house
value allowed by the bank based on PTI and LTV considerations lowers the
value of the purchased house, but only by 0.43%. The parameter estimates
for the unconstrained households are similar to our results in column 1,
but the permanent income elasticity is now equal to 1.24 and
significantly above 1.
For reasons discussed above, we again limit the sample to
first-time home buyers with head age 34 or younger, reducing the sample
from 2,364 to 703 households. Column 10 mostly confirms the results of
column 9. The difference is that the permanent income coefficient is now
no longer significantly different from i. As is the case with the
previous age-restricted regressions, and may be related to the reduced
sample size, the precautionary variable becomes insignificant but
retains a value that is consistent with the precautionary variable
coefficients of the non-age-restricted regressions. Thus, again the age
restriction appears to strengthen the case for the LCPI (without
liquidity constraints).
A possible explanation for the constrained household results may be
related to the fact that banks, in the case of constrained households,
do have some effect on the value of the house purchased as follows from
columns 9 and 10. This could explain the lower permanent income
elasticity for the constrained households found in columns 6 and 7.
Since the results in columns 6 and 7 fail to identify a
household-initiated concern for future liquidity, it follows, with the
proviso that our data limitations may have introduced biases, that the
results in Table II, columns 1 and 2, reveal a true precautionary
savings effect on current consumption related to variability in lifetime
income, that is unrelated to liquidity considerations.
V. CONCLUSION
Households that face no current liquidity constraints and should
have relatively costless access to liquidity in the future, make housing
choices in accordance with an extended version of the LCPI that allows
for precautionary savings. As such, we add to the results of Jones
[1990], Bernanke [1984], and Hayashi [1985] by focusing initially only
on non-liquidity-constrained consumers in the "Unconstrained
Households" subsection of Section IV so that the precautionary and
liquidity effects may be separated.
Our results allow a reinterpretation of the Jones [1990]
observation that net wealth matters separately from lifetime income. He
concludes that the importance of net wealth points to liquidity
constraints. However, we note that higher net wealth also implies less
permanent income variability, so that the importance of net wealth could
point to precautionary motives just as easily as to liquidity
constraints. We provide some evidence for the precautionary motive and
preliminarily distinguish the precautionary motive explanation from the
liquidity constraint explanation by providing additional evidence
against the importance of household-initiated liquidity effects (based
on the absence of differences between unconstrained and
liquidity-constrained borrowers, and between liquidity-constrained ARM
and FRM holders, regarding the income uncertainty variable). We further
find that the minor liquidity problems that appear to exist may be bank
initiated, as a way to mitigate the effects of informational
asymmetries, rather than household initiated. A conclusion that
liquidity constraints have only a minor impact on housing choice is
further supported by the fact that banks seem to pay only limited
attention to the PTI and LTV indicators of liquidity constraints.
Our results suggest that precautionary savings may explain results
previously attributed to liquidity constraints. These results can only
be preliminary due to data limitations. In particular, the lack of
direct observations on income variability prohibits a definitive
separation of liquidity and precautionary effects. Given that Haurin
[1991], with more appropriate data, did not identify an effect of income
uncertainty on housing demand, further work is necessary to obtain
clarity on this issue. In addition, the problem of approximating wealth
with the down payment may invalidate our results. Restricting the sample
to young first-time home buyers deals in part with this problem, but the
precautionary effect now becomes insignificant, likely due to small
sample size. Finally, the restriction of our sample to home owners alone
may provide a bias that is only partly corrected by truncation of
housing values below a threshold value and then correcting for the known
bias.
Although our data are limited in these dimensions, the results at
least are robust in the face of attempts to correct biases; they further
allow a look at the life cycle hypothesis from a novel perspective.
Future work may apply panel data from the Survey of Consumer Finances in
the context of our model to obtain further evidence that may help to
separate the precautionary motive from liquidity constraint effects.
(*.) The authors thank two anonymous referees for very helpful
comments; one referee in particular provided extensive and constructive
comments that substantially improved the empirical part of the paper.
Balvers: Professor of Economics, West Virginia University,
Morgantown
Szerb: Associate Professor, Janus Pannonius University,
P[acute{e}]cs, Hungary.
(1.) This is not to say that earlier work in the housing literature
has not addressed the precautionary motive. In particular, Plaut [1987]
considers theoretically the precautionary savings that help absorb the
risk inherent in owning a house; Haurin and Gill [1987] and Haurin
[1991] consider empirically the effect of income uncertainty on housing
consumption.
(2.) Although lifetime should typically be viewed as stochastic as
well, it would be possible given perfect insurance markets to buy an
actuarially fair annuity that guarantees the level of consumption
derived here but for the stochastic lifetime (see also Caballero [1991,
870] for a similar argument). All decisions then would be identical.
Note that income insurance is a very different issue because severe
moral hazard and adverse selection problems make a perfect market for
such insurance highly implausible.
(3.) It is easy to check that utility can be increased for a given
budget if consumption is not smoothed perfectly before the income
uncertainty is resolved. A similar argument applies to guarantee perfect
consumption smoothing after the income uncertainty is resolved.
(4.) Notice that for r [rightarrow] 0 the use of
L'H[hat{o}]pital's rule implies that PI = [[W.sub.0] + sY + (R
- s)[eta]Y]/T.
(5.) We have experimented with including the following additional
variables in equation (14): an unemployment rate variable (varying by
region and by year) obtained from the Current Population Survey to
better capture income uncertainty. This variable turned out to be
insignificant, often with the wrong (positive) sign, in all regressions.
We also considered the square of age as an additional variable to
capture life cycle effects. This variable was usually significantly
negative as expected but did not have an important effect on the
coefficients of the other variables, and is not included. Regional
dummies were considered but then dropped from our regressions, since
their explanatory power is fully subsumed by the price variable.
(6.) Skinner [1994] reports that housing equity for the median
household is around 60% of total current wealth. Assuming that, for the
typical household, current wealth accumulates after the initial down
payment, the approximation of current wealth at the time of the home
purchase by the down payment appears to be reasonable. The results of
Duca and Rosenthal [1993] imply that current wealth and debt would be
positively correlated. Our assumption here, equating the down payment
with current wealth, implies that, for a given house size, current
wealth and mortgage debt are negatively correlated. However, since
current wealth is positively correlated with lifetime income, higher
current wealth also implies a more expensive house purchase so that
mortgage debt may be positively related to current wealth in our model
as well.
(7.) These rather arbitrary parameter choices have little effect on
the empirical results. Checking the robustness of the main model we use
r = .02 and r = .04, s = 3 and s = 7 instead and find no qualitative
changes in our results. Similarly we set initial wealth at twice the
down payment (instead of equal to the down payment) and find no
qualitative changes in our results.
(8.) We calculate the mortgage rate in the PTI constraint using the
FRM rate (varying only by month and by region) for all households. This
avoids the endogeneity problem arising if households choose the ARM,
with, typically, an initially lower rate, to avoid becoming constrained.
Results when the actual rate paid by the household is used in
calculating the PTI are not presented but are similar in all respects to
the results presented below. Similarly, in our probit regression for the
prudence proxy, we use average FRM and ARM rates (varying only by month
and by region) to avoid the problem that, for individual households,
only the actual rate for the chosen mortgage type is available.
(9.) As discussed in Phillips and Vanderhoff [1994, 459], banks
require a maximum LTV ratio that is in all cases 0.90 or higher. Banks
also require a PTI ratio of no more than 0.28. See for instance
Brueckner and Follain [1989].
(10.) The fact that no renters are included in the sample causes a
potential sample selection bias that, as for example, in Jones [1990],
we cannot easily correct. Households desiring small homes may be more
likely to rent and, if their housing demand has a negative
"error" component, are less likely to be in the sample. As
this is more likely to occur at low permanent income levels, the
estimate of the permanent income elasticity may be biased downward. One,
imperfect, way to correct for the bias is to truncate the sample to
eliminate all low house values and then correct for the truncation bias.
When we do this in the regressions of columns 1 and 2 for threshold
house values of $50,000 and $80,000, we find very little impact on the
coefficient estimates; the permanent income coefficients are higher in
all cases but negligibly so. Thus, it appears that the sample selection
bias due to absence of renters is minor.
(11.) As discussed by Henderson and loannides [1983], portfolio
considerations contribute to households having different consumption and
investment demands for housing. Observed housing may therefore not
reflect a consumption demand for housing. Ioannides and Rosenthal [1994]
show however that, empirically, the residence of most homeowners is
determined primarily by their consumption demand.
REFERENCES
Bernanke, Ben. "Permanent Income, Liquidity and Expenditure on
Automobiles: Evidence from Panel Data." Quarterly Journal of
Economics, 99, 1984, 587-614.
Brueckner, Jan, and James Follain. "ARMs and the Demand for
Housing." Regional Science and Urban Economics, 19, 1989, 163-87.
Caballero, Ricardo. "Consumption Puzzles and Precautionary
Savings." Journal of Monetary Economics, 25, 1990, 113-136.
_____. "Earnings Uncertainty and Aggregate Wealth
Accumulation." American Economic Review, 81, 1991, 859-71.
Deaton, Angus. Understanding Consumption. Oxford: Oxford University
Press, 1992.
Duca, John V., and Stuart S. Rosenthal. "Borrowing
Constraints, Household Debt, and Racial Discrimination in Loan
Markets." Journal of Financial Intermediation, 3, 1993, 77-103.
Friedman, Milton. A Theory of the consumption Function, Princeton,
N.J.: Princeton University Press, 1957.
Goldfeld, S. M., and R. E. Quandt. "Estimation in a
Disequilibrium Model and the Value of Information." Journal of
Econometrics, 3, 1975, 325-48.
Grossman, Sanford J., and Guy Laroque. "Asset Pricing and
Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption
Goods." Econometrica, 58, 1990, 25-52.
Hall, Robert E., and Frederic S. Mishkin. "The Sensitivity of
Consumption to Transitory Income: Estimates from Panel Data on
Households." Econometrica, 50, 1982, 461-81.
Harrington, David. "An Intertemporal Model of Housing Demand:
Implications for the Price Elasticity." Journal of Urban Economics,
25, 1989, 230-46.
Haurin, Donald R. "Income Variability, Homeownership, and
Housing Demand." Journal of Housing Economics, 1, 1991, 60-74.
Haurin, Donald R., and H. Leroy Gill. "Effects of Income
Variability on the Demand for Owner-Occupied Housing." Journal of
Urban Economics, 22, 1987, 136-50.
Hayashi, Fumio. "The Effect of Liquidity Constraints on
Consumption: A Cross-Sectional Analysis." Quarterly Journal of
Economics, 100, 1985, 183-206.
Henderson, J. Vernon, and Yannis M. Ioannides, "A Model of
Housing Tenure Choice." American Economic Review, 73, 1983, 98-113.
Hubbard, Glenn, Jonathan Skinner, and Stephen Zeldes.
"Precautionary Saving and Social Insurance." Journal of
Political Economy, 103, 1995, 360-99.
loannides, Yannis M., and Stuart S. Rosenthal. "Estimating the
Consumption and Investment Demands for Housing and their Effect on
Housing Tenure Status." Review of Economics and Statistics, 76,
1994, 127-41.
Jones, Lawrence D. "Current Wealth Constraints on the Housing
Demand of Young Owners." Review of Economics and Statistics, 72,
1990, 424-32.
Kimball, Miles S. "Precautionary Saving in the Small and in
the Large." Econometrica, 58, 1990, 53-74.
Maddala, G. S. Limited-Dependent and Qualitative Variables in
Econometrics, Cambridge: Cambridge University Press, 1983.
Modigliani, Franco, and Richard Brumberg. "Utility Analysis
and the Consumption Function," in Post Keynesian Economics, edited
by K. Kurihara. London: G. Allen, 1954, 388-436.
Phillips, Richard A., and James H. Vanderhoff. "Alternative
Mortgage Instruments, Qualification Constraints and the Demand for
Housing: an Empirical Analysis." Journal of the American Real
Estate and Urban Economics Association, 21, 1994, 453-77.
Plaut, Steven E. "The Timing of Housing Tenure
Transition." Journal of Urban Economics, 21, 1987, 312-22.
Sacher, Scth. "Housing Demand and Property Tax Incidence in a
Life-Cycle Framework." Public Finance Quarterly, 21, 1993, 235-59.
Sheiner, Louise. "Housing Prices and the Savings of
Renters." Journal of Urban Economics, 38, 1995, 94-125.
Skinner, Jonathan. "Housing and Saving in the United
States," in Housing Markets in the United States and Japan, edited
by Yukio Noguchi and James M. Poterba. National Bureau of Economic
Research Conference Report. Chicago: University of Chicago Press, 1994,
191-213.
Szerb, L[acute{a}]szl[acute{o}]. "The Borrower's Choice
of Fixed and Adjustable Rate Mortgages in the Presence of Nominal and
Real Shocks." Journal of the American Real Estate and Urban
Economics Association, 24, 1996, 43-54.
Xu, Xiaonian. "Precautionary Savings under Liquidity
Constraints: A Decomposition." International Economic Review, 36,
1995, 675-90.
Zeldes, Stephen. "Optimal Consumption with Stochastic Income:
Deviations from Certainty Equivalence." Quarterly Journal of
Economics, 54, 1989, 275-98.
Summary Statistics
All Households Unconstrained
Standard Standard
Variable Mean Deviation Mean Deviation
House value 125,221 89,478 141,992 87,920
(dollars)
Down payment 29,627 44,243 57,636 59,727
(dollars)
After-tax income 40,912 18,690 46,234 19,774
(dollars per annum)
Permanent income 32,934 15,248 36,276 16,532
(dollars per annum)
Coefficient of variation 0.69 0.17 0.62 0.21
permanent income
Age 36.0 9.1 40.2 9.59
(years)
Household size 2.76 0.98 2.76 0.80
(units)
Loan-to-value 0.81 0.16 0.62 0.14
(fraction)
Payment-to-income 0.18 0.07 0.14 0.05
(fraction)
Mortgage rate 9.84 0.73 9.90 0.68
(percentage)
Sample size 2,364 -- 616 --
(units)
ARM Holders
Standard
Variable Mean Deviation
House value 158,470 115,185
(dollars)
Down payment 37,572 49,429
(dollars)
After-tax income 43,887 20,151
(dollars per annum)
Permanent income 35,726 16,570
(dollars per annum)
Coefficient of variation 0.69 0.16
permanent income
Age 36.0 8.8
(years)
Household size 2.66 1.08
(units)
Loan-to-value 0.80 0.13
(fration)
Payment-to-income 0.18 0.08
(fraction)
Mortgage rate 8.65 0.68
(percentage)
Sample size 457 --
(units)
Note: Unconstrained households are defined as those with a house
value less than 95% of the value obtainable given a maximum loan-
to-value ratio of 0.80 and a maximum payment-to-income ratio of 0.25.
Unconstrained Households
Variable 1 2 3 4
Constant 3.76 4.01 2.26 3.68
(7.68) (4.38) (13.30) (2.10)
Log of price index 0.59 0.63 0.45 0.33
[[p.sup.H].sub.i] (6.54) (3.46) (14.68) (3.43)
Log of permanent income 0.94 0.92 1.02 0.91
E([PI.sub.i]) (20.72) (10.81) (60.11) (17.47)
PI variability -1.37 -0.98 -1.42 -1.25
[[gamma].sub.i] (7.29) (3.06) (17.90) (1.71)
Age -0.01 -0.01 -0.00 -0.03
[T.sub.i] (3.02) (1.60) (2.11) (2.89)
Household size -0.03 -0.01 -0.03 -0.02
[HS.sub.i] (1.58) (0.11) (3.80) (1.08)
(Mortgage type error) * -- -- -- --
(PI Var.) [[omega].sub.i][[gamma].sub.i]
Average house size 126 142 125 97
[[p.sup.H].sub.i][H.sub.i]
Sample size 1605 616 2364 352
Variable 5
Constant 3.76
(7.80)
Log of price index 0.58
[[p.sup.H].sub.i] (6.41)
Log of permanent income 0.94
E([PI.sub.i]) (20.68)
PI variability -1.29
[[gamma].sub.i] (6.53)
Age -0.01
[T.sub.i] (2.99)
Household size -0.03
[HS.sub.i] (1.53)
(Mortgage type error) * -0.10
(PI Var.) [[omega].sub.i][[gamma].sub.i] (1.43)
Average house size 126
[[p.sup.H].sub.i][H.sub.i]
Sample size 1605
Notes: Absolute t-statistics in parentheses. The independent
variable is in all cases the log of the purchase price of the house. All
equations except for column 3 are estimated by maximum likelihood
corrected for truncation bias using the Newton method for computing standard errors. Column 1 displays the regression result based on
equation (15) for the sample of unconstrained households whose house
value is less than 95% of the maximum feasible given LTV [less than]
0.95 and PTI [less than] 0.28. Column 2 displays the result for the
sample of unconstrained households with house value less than 95% of the
maximum feasible given LTV [less than] 0.80 and PTI [less than] 0.25.
Column 3 displays the OLS regression results for the full sample. Column
4 considers the sample in column 1 further restricted to exclude
households with head age exceeding 34 years and those who are not
first-time home buyers. In column 5, the interaction dummy variable for
mortgage choice (ARM = 0) with permanent income uncertainty is a dded
for the sample in column 1.
Constrained Households
Variable 6 7 8 9 10
Constant 4.48 3.47 1.10 0.84 3.83
(7.80) (12.38) (0.96) (2.81) (2.89)
Log of price index 0.32 0.32 0.30 0.67 0.36
[[p.sup.H].sub.i] (4.00) (6.81) (5.38) (12.64) (6.66)
Log of permanent income 0.73 0.84 0.87 1.24 0.95
E([PI.sub.i]) (12.56) (30.18) (24.48) (36.95) (25.45)
PI variability -0.82 -0.84 -0.97 -1.86 -1.45
[[gamma].sub.i] (2.95) (6.89) (0.80) (13.64) (1.09)
Age [T.sub.i] -0.00 -0.00 -0.03 -0.01 -0.04
(0.01) (0.36) (5.71) (3.48) (6.67)
Household size [HS.sub.i] -0.03 -0.02 -0.03 -0.04 -0.04
(1.64) (2.00) (2.34) (3.63) (3.33)
(Mortgage type error)* -0.12 -0.05 -0.04 -- --
(PI Var.) [[omega].sub.i] (1.33) (1.29) (0.93)
[[gamma].sub.i]
Constant [c.sub.0] -- -- -- 6.85 8.21
(47.28) (29.51)
Bank max [c.sub.1] -- -- -- 0.43 0.33
(35.09) (13.52)
Average house size 114 112 87 125 91
[[p.sup.H].sub.i][H.sub.i]
Sample size 565 1,298 553 2,364 703
Notes: The independent variable is in all eases the log of the
purchase price of the house. Equations are estimated by maximum
likelihood. Columns 6, 7, and 8 are corrected for truncation bias using
the Newton method for computing standard errors. Columns 6 and 7 display
the regression results based on equation (15) for the sample of
constrained households (with house price larger than 105% of the maximum
value, given LTV [geq] 0.80 and PTI [geq] 0.25, and LTV [geq] 0.95 and
PTI [geq] 0.28, respectively). Column 8 represents the same regression
as in column 7 with the sample further limited to households with head
age less than 35 who are first-time home buyers. Columns 9 and 10 use
the endogenous switching likelihood function as given by Maddala [1983,
eq. (10.21)] and present the results based on equations (15) and (16),
for the full sample in column 9 and, for first-time home buyers under 35
years old, in column 10.
ABBREVIATIONS
ARM: adjustable-rate mortgage
CES: constant elasticity by substitution
CFVR: coefficient of variation of permanent income
CRRA: constant relative risk aversion
FRM: fixed-rate mortgage
LCPI: life cycle/permanent income [hypothesis]
LTV: loan to value [ratio]
MIRS: Mortgage Insurance Rate Survey
OLS: ordinary least squares
PTI: payment to income [ratio]
APPENDIX
The Determinants of Precautionary Savings
Taking expectations on both sides of equation (8) yields
(Al) Z = E(PI)/q,
where q [equiv] 1 + f(T)E(Q) and f(T) [equiv] [[(1 + r).sup.T-s] -
1]/[[(1 + r).sup.T] - 1]. Since PI = E(PI) + [epsilon] we can write by
definition of the coefficient of variation, [gamma], that
(A2) PI = (1 + [gamma][kappa])E(PI),
where [kappa] is a standardized random variable with mean zero and
variance of one. Substitute equations (8), (Al) and (A2) into equation
(12) to obtain
(A3) U'[lgroup][frac{E(PI)}{q}][rgroup]
= E{U'[E(PI)[lgroup][frac{f(T) - 1 + q}{f(T)q}] +
[frac{[gamma][kappa]}{f(T)}][rgroup]]}.
From (A3) we thus have in general that q = q[[gamma], E(PI), T,
[omega]], where [omega] is a shift variable of the utility function U,
but we also want to establish the direction of the effect that these
variables have on q.
An increase in [gamma] (all else equal) implies a mean preserving
spread of the function argument on the right-hand side of (A3). Under
"prudence" U'( ) is convex so that the r.h.s. of (A3)
increases. Thus the l.h.s. should increase as well implying that q
increases, since U( ) is concave, so that [q.sub.[gamma]] [greater than]
0. Similarly, an increase in prudence ([omega] increases) raises q,
[q.sub.[omega]] [greater than] 0.
The effects of E(PI) and T are more complex. To examine these, we
assume constant relative risk aversion for the utility function (which
implies prudence). It is clear from (A3) that E(PI) drops from both
sides if CRRA is assumed. Thus, [q.sub.E(PI)] = 0. Even under CRRA the
effect of T cannot be signed: [q.sub.T] [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] are stated in the text.